# Math 160: Study Guide - Chapters 7-8

1. You are given a joint frequency table and asked to identify the number in an event.
2. You are given portions of a joint probability distribution and enough information to complete the table.
3. You are given a joint probability distribution. Use it to find the indicated probabilities.
4. Complete the truth table.
5. Decision Analysis problem. A payoff table is given. Compute the opportunistic loss table. Find the payoff or loss under the expected value, maximax, maximin, and minimax criterions.
6. Determine the number of ways certain events can happen using combinations.
7. Determine the number of ways certain events can happen.
8. You are given the probabilities of some events. Use the multiplication rule to find the probabilities of compound events. For example, you may be given the probabilities of events A, B, and C and asked to find the probability that all three occur or that A and B but not C occur, etc.
9. A bag contains different types of bills. Find the probability of a randomly selected bill being of a particular kind. Find the probability of the second bill being of a particular kind if you replace the first, don't replace the first but know what it was, and don't replace the first and don't know what it was.
10. Bayesian problem. Create a joint probability distribution from the information given. Then find some probabilities. Some of the probabilities are marginals, some are joint, some are conditional. You need to be able to figure out which is which by reading the problem.
11. Find the number of ways a certain poker hand can occur. The problem has been modified by removing some of the cards from the deck, so be careful. Show the setup if you want partial credit. You may use the hypergeometric program to find the values, but you only want the numerator. These are simpler probabilities, not things like "full house" or "three of a kind".
12. Finish a series of a game. Create a tree diagram, find the probability that the series goes until a certain number of games, find the probability each team wins.

## Notes

• Portions of problems 10-12 will be sent home with you prior to the actual exam. There are problems there that will need to be set up and completed before the actual exam. You will use the results of the take home exam to answer more questions on the in-class exam. If you try to wait until the actual exam to complete all of the exam, you will run out of time.
• You are encouraged to work in a group to complete the portion sent home with you to ensure you have the correct answers. You may work in groups of up to three people on the take-home portion.
• In the points per problem below, the notation 6+7 means that 6 points will be from the in-class portion and 7 points will be from the take-home portion.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 Total 5 4 14 8 10 4 4 4 6 10+6 12 6+7 100